A new hybrid mixed finite element method to solve acoustic fluid-structure interaction problems

Alan Amad¹; Iury Igreja¹; Thiago Quinelato¹; Abimael Loula¹

¹ LNCC/MCTI

doi:10.20906/CPS/CILAMCE2015-0624

Resumo

Fluid-structure interactions (FSI) modeling is an important problem with applications in geophysics and engineering, including vibration and structural dynamic response, dam failures during seismic excitation, reductions in noise emissions, noise prediction in aeroacoustic and so on. In this work we develop a new stabilized hybrid mixed finite element method to solve the acoustics FSI problems. Hybrid methods are characterized by the introduction of Lagrange multipliers to weakly impose continuity on the interelement interfaces. This approach generates a global system involving only the degrees-of-freedom associated with the multipliers. The quantities of interest are obtained from local problems that are solved at the element level. In this context, to generate the hybrid method for the coupled fluid-structure problem we combine the hybrid formulations for the Helmholtz problem and the time-harmonic elastic wave problem. This methodology allows for natural coupling of the fluid-structure interface conditions via Lagrange multipliers. Results of some numerical experiments illustrating the flexibility and the robustness of the proposed finite element formulation are presented.

Palavras-chave: Mixed-Hybrid Methods; Helmholtz Problem; Time-Harmonic Elastic Wave Problem; Interface Conditions; Acoustics Fluid-Structure Interactions